Strictly stationary solutions of multivariate ARMA equations with i.i.d. noise
Statistics Theory
2011-05-19 v1 Probability
Statistics Theory
Abstract
We obtain necessary and sufficient conditions for the existence of strictly stationary solutions of multivariate ARMA equations with independent and identically distributed noise. For general ARMA equations these conditions are expressed in terms of the characteristic polynomials of the defining equations and moments of the driving noise sequence, while for an additional characterization is obtained in terms of the Jordan canonical decomposition of the autoregressive matrix, the moving average coefficient matrices and the noise sequence. No a priori assumptions are made on either the driving noise sequence or the coefficient matrices.
Keywords
Cite
@article{arxiv.1105.3510,
title = {Strictly stationary solutions of multivariate ARMA equations with i.i.d. noise},
author = {Peter J. Brockwell and Alexander Lindner and Bernd Vollenbroeker},
journal= {arXiv preprint arXiv:1105.3510},
year = {2011}
}